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• Level: GCSE
• Subject: Maths
• Word count: 3452

# T-Total Maths

Extracts from this document...

Introduction

Atif Eshaque Kamal

T-TOTAL

INTRODUCTION

In this coursework. I will be investigating the difference between T-Total and T-number. I am going to do this by doing different grids and in different angles. Then I will compare them to see the difference and what is common in each one of them .I am going to draw a T-shape inside the grid. The number, which will be at the bottom on T, is called T-Number. Counting all the numbers inside T will give T-Total. I am going to show you by drawing grid and plotting which is T-Total and T-Number.

ALL THE NUM

IN THE T ARE

T-TOTAL

THIS IS T-NUMBER

##### INVESTIGATION

I am going to be investigating the grids and the T-shape inside the grid. Which I have drawn underneath. The things I will be investigating and finding out are the formula for each of the grid and checking the pattern and what is common things in the formula of each of the grid. I will also find the algebraic way of working the formula. Lastly I will move the T-Shape in different angles.

The grids below will help me in my investigation. From these grids I will find the pattern of the formulas and a common formula that goes in every grid which l have done below.

## GRIDS – 5

 T NUMBER T-TOTAL 12 25 13 30 14 35
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
 12 1 2 3 7 13 2 3 4 8 14 3 4 5 9

Numbers inside Tshape

 T NUMBER T TOTAL 14 28 15 33 16 38 17 43
 5 X 12 = 60 – 25= 35 FORMULA= 5N - 35

### GRID-6

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

Numbers inside T shape

 14 1 2 3 8 15 2 3 4 9 16 3 4 5 10 17 4 5 6 11
 5 X 14 = 70 – 28= 42 FORMULA= 5N - 42
##### GRID 7
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 39 40 41 42 43 43 44 45 46 47 48 49 T NUMBER T TOTAL 16 31 17 36 18 41 19 46 20 57

Numbers inside T shape

 16 1 2 3 9 17 2 3 4 10 18 3 4 5 11 19 4 5 6 12 20 5 6 7 13
 5 X 16 = 80 – 39= 49 FORMUAL =5N - 49

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## T TOTAL

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34

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39

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49

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59

Numbers inside T shape

 18 1 2 3 10 19 2 3 4 11 20 3 4 5 12 21 4 5 6 13 22 5 6 7 14 23 6 7 8 15
 5 X 18 = 90 – 34= 56 FORMULA = 5N – 56

### GRID-9

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 T NUMBER T TOTAL 20 37 21 42 22 47 23 52 24 57 25 62 26 67

Numbers inside T shape

 20 11 1 2 3 21 12 2 3 4 22 13 3 4 5 23 14 4 5 6 24 15 5 6 7 25 16 6 7 8 26 17 7 8 9
 5 X 20 = 100 – 37 = 63 FORMUAL 5N – 63

### GRID-10

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 FORMULA USING 5N – 35 5 X 23 = 115 – 80= 35

### GRID 6

 T NUMBER T TOTAL 28 98
 28 22 15 16 17
 FORMULA USING 5N – 42 5 X 28 = 140 – 98= 42

### GRID 7

 T NUMBER T TOTAL 39 149
 39 32 24 25 26
 FORMULA USING 5N – 49 5 X 93 = 195 – 146= 49

### GRID 8

 T NUMBER T TOTAL 54 214
 54 46 37 38 39
 FORMULA USING 5N – 56 5 X 54 = 270 – 214= 56
 T NUMBER T TOTAL 59 232

## GRID 9

 59 50 40 41 42
 FORMULA USING 5N – 63 5 X 59 = 295 – 232= 63

### GRID 10

 T NUMBER T TOTAL 76 310
 76 66 56 55 57
 FORMULA USING 5N – 70 5 X 76 = 380 – 310= 70

I have done the checking and it shows that I have put in the correct formula that goes in each grid.

I am going to investigate the pattern in formula and find the common number from the grids formula. Below are the T-Number and T-Total and the numbers.

## GRIDS – 5

 T NUMBER T-TOTAL 12 25 13 30 14 35

Numbers inside T shape

 12 1 2 3 7 12 13 2 3 4 8 13 14 3 4 5 9 14 5 X 12 = 60 – 25= 35 FORMULA= 5N - 35
 T NUMBER T TOTAL 14 28 15 33 16 38 17 43

GRID-6

Numbers inside T shape

 14 1 2 3 8 14 15 2 3 4 9 15 16 3 4 5 10 16 17 4 5 6 11 17
 5 X 14 = 70 – 28= 42 FORMULA= 5N - 42

#### GRID 7

 T NUMBER T TOTAL 16 31 17 36 18 41 19 46 20 57

Numbers inside T shape

 16 1 2 3 9 17 2 3 4 10 18 3 4 5 11 19 4 5 6 12 20 5 6 7 13
 5 X 16 = 80 – 39= 49 FORMUAL =5N - 49

#### GIRD-8

Numbers inside T shape

## T TOTAL

18

34

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39

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49

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 5 X 18 = 90 – 34= 56 FORMULA = 5N – 56
 T NUMBER T TOTAL 20 37 21 42 22 47 23 52 24 57 25 62 26 67

#### GRID-9

Numbers inside T shape

 20 11 1 2 3 21 12 2 3 4 22 13 3 4 5 23 14 4 5 6 24 15 5 6 7 25 16 6 7 8 26 17 7 8 9
 5 X 20 = 100 – 37 = 63 FORMUAL = 5N – 63 T NUMBER T TOTAL 22 40 23 45 24 50 25 55 26 60 27 65 28 70 29 75

GRID 10

Numbers inside T shape

 22 1 2 3 12 23 2 3 4 13 24 3 4 5 14 25 4 5 6 15 26 5 6 7 16 27 6 7 8 17 28 7 8 9 18 29 8 9 10 19
 5 X 22 = 110 – 40=70 FORMULA=5N – 70
###### FORMULAS

GRID 5     = 5N - 35

GRID 6     = 5N - 42

GRID 7      =5N - 49

GRID 8       = 5N – 56

GRID 9       = 5N – 63

GRID 10      =5N – 70

PATTERN =35, 42, 49, 56, 63, 70

This shows that is it going up by 7 and it a multiple of 7.

COMMON = 5N because they all start with 5N and it the difference is 5 as well.

All the grids above formula begin with 5N because that how many numbers inside the T-shape. Number 7 links the endings of each formula because all the grids I have done its T-Total are multiples of 7.it also gives me the last part of the formula. Which I shown above.

FORMULA THAT GOES IN EACH GRID

I have found the formula that will help me find T-Total of any grid.

FORMULA = 5N – 7W

(N = T NUMBER)

(W = WIDTH OF GRID)

I will show you working out of each grid using the formula above, which will give me the T-Total of any grid.

WORKING OUT: -

GRID - 5

5 X 14 = 70

7 X 6 = 42

70 – 42

T-TOTAL = 25

GRID - 6

5 X 14 = 70

7 X 6 = 42

70 – 42

T-TOTAL = 28

GRID 7

5 X 16 = 80

7 X 7 = 49

80 – 49

T-TOTAL = 31

GRID 8

5 X 18 = 90

7 X 8 = 42

90 – 42

T-TOTAL = 34

GRID 9

5 X 20 = 100

7 X 9 = 63

100 – 63

T-TOTAL = 37

GRID 10

5 X 22 = 110

7 X 10 = 70

110 – 70

T-TOTAL = 40

As you can see above. That my calculation prove that I have found the

T-Total of any number using the formula (5N – 7W).

MOVING THE T UPSIDEDOWN

## GRIDS – 5

 T NUMBER T-TOTAL 2 45 3 50 4 55

Numbers inside T shape

 2 7 11 12 13 3 8 12 13 14 4 9 13 14 15
 5 X 2 = 10 – 45= - 35 FORMULA= 5N + 35

GRID-6

 T NUMBER T TOTAL 2 52 3 57 4 62 5 67

Numbers inside T shape

 2 8 13 14 15 3 9 14 15 16 4 10 15 16 17 5 11 16 18 19
 5 X 2 = 10 – 52= - 42 FORMULA= 5N + 42

### GRID 7

 T NUMBER T TOTAL 2 59 3 64 4 69 5 74 6 79

Numbers inside T shape

 2 9 15 16 17 3 10 16 17 18 4 11 17 18 19 5 12 18 19 20 6 13 17 20 21
 5 X 2 = 10 – 39= - 49 FORMUAL =5N + 49

### GIRD-8

Numbers inside T shape

## T TOTAL

2

66

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71

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76

5

81

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86

7

91

 2 10 17 18 19 3 11 18 19 20 4 12 19 20 21 5 13 20 21 22 6 14 21 22 23 7 15 22 23 24
 5 X 2 = 10 – 66= - 56 FORMULA = 5N + 56

#### GRID-9

 T NUMBER T TOTAL 2 73 3 78 4 83 5 88 6 93 7 98 8 103

Numbers inside T shape

 2 11 19 20 21 3 12 20 21 22 4 13 21 22 23 5 14 22 23 24 6 15 23 24 25 7 16 24 25 26 8 17 25 26 27
 5 X 2 = 10 – 73 = - 63 FORMUAL = 5N + 63
##### GRID-10
 T NUMBER T TOTAL 2 80 3 85 4 90 5 95 6 100 7 105 8 110 9 115

Conclusion

GRID 9

N + N-1 - N-2 – N-11 + N+7 (FORMULA=5N-7)

GRID 10

N + N-1 - N-2 – N-12 + N+8 (FORMULA=5N-7)

TURNING T RIGHT

GRID 5

N + N+1 + N+2 + N+7 – N-3 (FORMULA=5N+7)

GRID 6

N + N+1 + N+2 + N+8 – N-4 (FORMULA=5N+7)

GRID 7

N + N+1 + N+2 + N+9 – N-5 (FORMULA=5N+7)

GRID 8

N + N+1 + N+2 + N+10 – N-6 (FORMULA=5N+7)

GRID 9

N + N+1 + N+2 + N+11 – N-7 (FORMULA=5N+7)

GRID 10

N + N+1 + N+2 + N+12  - N-8 (FORMULA=5N+7)

In the grids above I have used algebra in the T shape to show that I can do working out in algebraic form. The difference was that T shape was + (positive) and when T shape was turned upside-down was – (negative).

When I turned T shape left and then right I found the formula that goes into both of the shapes was 5n-7.the only differences was that T shape which was turn left had a – (Negative) and the one turned was + (positive).

FINDING THE W BY W GRID

T SHAPE

N – N-W – N-2W – N-2W-1 – N-2W+1

TURNING T UPSIDE DOWN

N+ N+W + N+2W + N+2W+1 + N+2W-1

I have found that T shape and upside-down shape have the same w-by w formula that will give 5n-7w.Doing that formula I can work out and any number when I draw T shape and when I turn it up side down.

TURNING T LEFT

N + N-1 + N-2 + N+2+W + N-2+W

TURNING T RIGHT

N + N+1 + N+2  + N+2 – W + N+2+W

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